The ZEP, which ended on 31 December 2021, will not be extended.
Those with a permit have a 12-month grace period to either apply for another type of permit or leave the country.
Motsoaledi’s decision was supported by Cabinet.
“It is not the position of HSF that those migrants who are in South Africa unlawfully should be entitled to remain, nor even that the ZEP must continue in perpetuity,” the foundation said.
“Rather, our position is that those who have scrupulously observed South Africa’s laws in order to live and work here, under the ZEP, cannot have such permits terminated without fair process, good reason and a meaningful opportunity to regularise their status. It is what our constitutional order demands.”
In November 2021, Cabinet made the decision not to renew the ZEP.
It raised the ire of Zimbabweans and rights groups, who approached the court on an urgent basis. They were, however, unsuccessful.
Civil rights groups argued it would be impossible for current permit holders to successfully apply for other permits.
The foundation said: “This special dispensation regime has offered legal protection to approximately 178 000 Zimbabwean nationals, allowing them to live, work and study in South Africa. It has prevailed for well over a decade, meaning that permit-holders have built lives, families, and careers here, and contributed to South Africa and its economy.
“At present, ZEP holders must have obtained other forms of residency authorisation — in the vast majority of cases, an almost impossible requirement — by 31 December 2022 or leave South Africa.
“They will be put to a desperate choice: to remain in South Africa as undocumented migrants with all the vulnerability that attaches to such status or return to a Zimbabwe that, to all intents and purposes, is unchanged from the country they fled.
“There are thousands of children, who have been born in South Africa to ZEP holders during this time, who have never even visited their parents’ country of origin.”